GPU并行化持久同调计算的线性运行时间
Linear Run Time of Persistent Homology Computation with GPU Parallelization
摘要：
持久同源性是一个重要的不变量，在许多领域都用于理解数据。$O(N^4)$运行时间是它在大多数大型数据集上使用的一个障碍。我们给出了一种利用多核机器和集群的并行化方法。我们实现了$0^{th}$持久同源性的计算与OpenMP并行化，并观察到1.75倍的性能提高，使用2个线程的双核机器上。我们还基准的计算使用大量的线程，并表明线程的计算开销降低性能。通过GPU并行化，我们通过分析和经验将运行时间从$O(N^4)$扩展到$O(N^3)$，甚至是$O(N^2)$，其中$N$是足够大的GPU的数据点数量。接下来，我们分析显示运行时间缩放$O(N)$甚至更大的GPU。
英文摘要：
Persistent homology is a crucial invariant that is used in many areas to understand data. The $O(N^4)$ run time is a hindrance to its use on most large datasets. We give a parallelization method to utilize multi-core machines and clusters. We implement the computation of the $0^{th}$ persistent homology with OpenMP parallelization and observe a 1.75 fold performance increase by using 2 threads on a dual core machine. We also benchmark the computation using larger numbers of threads and show that the thread computational overhead decreases performance. With GPU parallelization, we analytically and empirically decrease the run time scaling from $O(N^4)$ to $O(N^3)$ and even $O(N^2)$ where $N$ is the number of data points, for a large enough GPU. Next, we analytically show run time scaling $O(N)$ for an even larger GPU.
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